Feeds:
Posts
Therein we find a very interesting analysis for this relation which is done directly on a compactified manifold $S^4$, which is very useful because it is quite possible that the issues involving quantizing Yang-Mills theories in this case is a completely solved problem.  Here is the reference where S4 calculations were done:  NielsenSchroerAxialAnomalyAtiyahSingerTheorem.  This is useful for the project of learning what has been already done for a consistent quantized gauge theory for a 4-sphere background.  There are several approaches to seeking the right physics.  One approach would be to ensure that the efforts for a quantized gauge theory with a mass gap are clear (for examply via geometric quantization with BRST cohomology for a compactification of the cotangent bundle of S4 or directly).  The more ambitious hope would be that one can directly construct a classical theory using classical Dirac and Yang-Mills fields on S4 with a coherence with gravity given by taking critical points of the Einstein-Hilbert action but along hypersurfaces.  This more ambitious approach would fulfill the idea that quantization itself is geometrically determined and there may not be a need to transplant QFT.  But the former approach is in line with the mainstream thrust of the field while the latter would be a radically different direction.